S2 Surface Quasi-3D Aerodynamic Design Using the Continuous Adjoint Method for Multi-Stage Turbine

The adjoint method eliminates the dependence of the gradient of the objective function with respect to design variables on the flow field making the obtainment of the gradient both accurate and fast. For this reason, the adjoint method has become the focus of attention in recent years. This paper develops a continuous adjoint formulation for through-flow aerodynamic shape design in a multi-stage gas turbine environment based on a S2 surface quasi-3D problem governed by the Euler equations with source terms. Given the general expression of the objective function calculated via a boundary integral, the adjoint equations and their boundary conditions are derived in detail by introducing adjoint variable vectors. As a result, the final expression of the objective function gradient only includes the terms pertinent to those physical shape variations that are calculated by metric variations. The adjoint system is solved numerically by a finite-difference method with explicit Euler time-marching scheme and a Jameson spatial scheme which employs first and third order dissipative flux. Integrating the blade stagger angles and passage perturbation parameterization with the simple steepest decent method, a gradient-based aerodynamic shape design system is constructed. Finally, the application of the adjoint method is validated through a 5-stage turbine blade and passage optimization with an objective function of entropy generation. The result demonstrates that the gradient-based system can be used for turbine aerodynamic design.

Non-Axisymmetric Turbine Endwall Aerodynamic Optimization Design: Part I — Turbine Cascade Design and Experimental Validations

The non-axisymmetric endwall profiling has been proven to be an effective tool to reduce the secondary flow loss in turbomachinery. In this work, the aerodynamic optimization for the non-axisymmetric endwall profile of the turbine cascade and stage was presented and the design results were validated by annular cascade experimental measurements and numerical simulations. The parametric method of the non-axisymmetric endwall profile was proposed based on the relation between the pressure field variation and the secondary flow intensity. The optimization system combines with the non-axisymmetric endwall parameterization method, global optimization method of the adaptive range differential evolution algorithm and the aerodynamic performance evaluation method using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) and k–ω SST turbulent with transition model solutions. In the part I, the optimization method is used to design the optimum non-axisymmetric endwall profile of the typical high loaded turbine stator. The design objective was selected for the maximum total pressure coefficient with constrains on the mass flow rate and outlet flow angle. Only five design variables are needed for one endwall to search the optimum non-axisymmetric endwall profile. The optimized non-axisymmetric endwall profile of turbine cascade demonstrated an improvement of total pressure coefficient of 0.21% absolutely, comparing with the referenced axisymmetric endwall design case. The reliability of the numerical calculation used in the aerodynamic performance evaluation method and the optimization result were validated by the annular vane experimental measurements. The static pressure distribution at midspan was measured while the cascade flow field was measured with the five-hole probe for both the referenced axisymmetric and optimized non-axisymmetric endwall profile cascades. Both the experimental measurements and numerical simulations demonstrated that both the secondary flow losses and the profile loss of the optimized non-axisymmetric endwall profile cascade were significantly reduced by comparison of the referenced axisymmetric case. The weakening of the secondary flow of the optimized non-axisymmetric endwall profile design was also proven by the secondary flow vector results in the experiment. The detailed flow mechanism of the secondary flow losses reduction in the non-axisymmetric endwall profile cascade was analyzed by investigating the relation between the change of the pressure gradient and the variation of the secondary flow intensity.

POD-Driven Adaptive Sampling for Efficient Surrogate Modeling and its Application to Supersonic Turbine Optimization

A new approach for adaptively sampling a design parameter space using an error estimate through the reconstruction of flow field by a combination of proper orthogonal decomposition (POD) and radial basis function network (RBFN) is presented. It differs from other similar approaches in that it does not use the reconstructed flow field by POD for the evaluation of objective functions, and thus it can be a subset of the flow field. Advantages of this approach include the ease of constructing a chain of simulation codes as well as the flexibility of choosing where and what to reconstruct within the solution domain. An improvement in achieving a good prediction quality, with respect to other adaptive sampling methods, has been demonstrated using supersonic impulse turbine optimization as the test case. A posteriori validation of the surrogate models were also carried out using a set of separately-evaluated samples, which showed a similar trend as the Leave-One-Out (LOO) cross-validation. The progressively enriched surrogate model was then used to achieve the more uniformly populated Pareto front with fewer number of function evaluations.

Sequential vs Multidisciplinary Coupled Optimization and Efficient Surrogate Modelling of a Last Stage and the Successive Axial Radial Diffuser in a Low Pressure Steam Turbine

In order to meet the requirements of rising energy demand, one goal in the design process of modern steam turbines is to achieve high efficiencies. A major gain in efficiency is expected from the optimization of the last stage and the subsequent diffuser of a low pressure turbine (LP). The aim of such optimization is to minimize the losses due to separations or inefficient blade or diffuser design. In the usual design process, as is state of the art in the industry, the last stage of the LP and the diffuser is designed and optimized sequentially. The potential physical coupling effects are not considered. Therefore the aim of this paper is to perform both a sequential and coupled optimization of a low pressure steam turbine followed by an axial radial diffuser and subsequently to compare results. In addition to the flow simulation, mechanical and modal analysis is also carried out in order to satisfy the constraints regarding the natural frequencies and stresses. This permits the use of a meta-model, which allows very time efficient three dimensional (3D) calculations to account for all flow field effects.

Automatic Three-Dimensional Optimisation of a Modern Tandem Compressor Vane

In order to increase the performance of a modern gas turbine, compressors are required to provide higher pressure ratio and avoid incurring higher losses. The tandem aerofoil has the potential to achieve a higher blade loading in combination with lower losses compared to single vanes. The main reason for this is due to the fact that a new boundary layer is generated on the second blade surface and the turning can be achieved with smaller separation occurring. The lift split between the two vanes with respect to the overall turning is an important design choice. In this paper an automated three-dimensional optimisation of a highly loaded compressor stator is presented. For optimisation a novel methodology based on the Multipoint Approximation Method (MAM) is used. MAM makes use of an automatic design of experiments, response surface modelling and a trust region to represent the design space. The CFD solutions are obtained with the high-fidelity 3D Navier-Stokes solver HYDRA. In order to increase the stage performance the 3D shape of the tandem vane is modified changing both the front and rear aerofoils. Moreover the relative location of the two aerofoils is controlled modifying the axial and tangential relative positions. It is shown that the novel optimisation methodology is able to cope with a large number of design parameters and produce designs which performs better than its single vane counterpart in terms of efficiency and numerical stall margin. One of the key challenges in producing an automatic optimisation process has been the automatic generation of high-fidelity computational meshes. The multi block-structured, high-fidelity meshing tool PADRAM is enhanced to cope with the tandem blade topologies. The wakes of each aerofoil is properly resolved and the interaction and the mixing of the front aerofoil wake and the second tandem vane are adequately resolved.

Through Flow Calculations for Convective Cooling Turbines

Conjugate heat transfer is a key feature of modern gas turbine, as cooling technology is widely applied to improve the turbine inlet temperature for high efficiency. Impact of conjugate heat transfer on heat loads and thermodynamic efficiency is a key issue in gas turbine design. This paper presented a through flow calculation method to predict the impact of heat transfer on the design process of a convective cooled turbine. A cooling model was applied in the through flow calculations to predict the coolant requirements, as well as a one-dimensional mixing model to evaluate some key parameters such as pressure losses, deviation angles and velocity triangles because of the injection cooling air. Numerical simulations were performed for verification of the method and investigation on conjugate heat transfer within the blades. By comparing these two calculations, it is shown that the through flow calculation method is a useful tool for the blade design of convective cooled turbines because of its simplicity and flexibility.

Simultaneous Robust Design and Tolerancing of Compressor Blades

The manufacturing processes used to create compressor blades inevitably introduce geometric variability to the blade surface. In addition to increasing the performance variability, it has been observed that introducing geometric variability tends to reduce the mean performance of compressor blades. For example, the mean adiabatic efficiency observed in compressor blades with geometric variability is typically lower than the efficiency in the absence of variability. This “mean-shift” in performance leads to increased operating costs over the life of the compressor blade. These detrimental effects can be reduced by using robust optimization techniques to optimize the blade geometry. The impact of geometric variability can also be reduced by imposing stricter tolerances, thereby directly reducing the allowable level of variability. However, imposing stricter manufacturing tolerances increases the cost of manufacturing. Thus, the blade design and tolerances must be chosen with both performance and manufacturing cost in mind. This paper presents a computational framework for performing simultaneous robust design and tolerancing of compressor blades subject to manufacturing variability. The manufacturing variability is modelled as a Gaussian random field with non-stationary variance to simulate the effects of spatially varying manufacturing tolerances. The statistical performance of the compressor blade system is evaluated using the Monte Carlo method. A gradient based optimization scheme is used to determine the optimal blade geometry and distribution of manufacturing tolerances.

Applications of Explicit Algebraic Reynolds Stress Models to Transonic Turbulence Flow Simulations Based on Discontinuous Galerkin Methods

Two applications of the non-linear eddy-viscosity model EARSM are presented in the simulations of transonic turbulent flow involving shock waves and other related complex features. The simulations are implemented applying an in-house CFD program based on the unstructured discontinuous Galerkin method, an alternative discretization method of the classical finite volume one to precisely capture the flow features. A series of turbulence feature variables in boundary layers are comparatively observed and analyzed. For the first case of transonic flow over a bump, the redistribution effect of Reynolds stress components rooted in the non-linear constitution relation promotes streamwise turbulence fluctuation and suppresses the normal one in boundary layer, comparing with the traditional linear constitution relation, especially when passing the shocks. The production magnitudes of the turbulence shear stress and kinetic energy for the non-linear model show slightly more sensitive to perturbations, such as the occurrence of shock front or compression corner, than the linear one. For the second case of a transonic turbine vane, similar redistribution effect of the non-linear model is also verified on suction surface around the strong shock. The straightforward redistribution effect is absent on pressure surface around middle part of the vane with favorable pressure gradients. There the non-linear model evaluates higher magnitudes of streamwise, normal and shear Reynolds stress components than the linear one, thus resulting locally stronger heat convection and higher surface temperature.

Accelerated 3D Aerodynamic Optimization of Gas Turbine Blades

State-of-the-art aerodynamic blade design processes mainly consist of two phases: optimal design of 2D blade sections and then stacking them optimally along a three-dimensional stacking line. Such a quasi-3D approach, however, misses the potential of finding optimal blade designs especially in the presence of strong 3D flow effects. Therefore, in this paper a blade optimization process is demonstrated which uses an integral 3D blade model and 3D CFD analysis to account for three-dimensional flow features. Special emphasis is put on shortening design iterations and reducing design costs in order to obtain a rapid automatic optimization process for fully 3D aerodynamic turbine blade design which can be applied in an early design phase already. The three-dimensional parametric blade model is determined by up to 80 design variables. At first, the most important design parameters are chosen based on a non-linear sensitivity analysis. The objective of the subsequent optimization process is to maximize isentropic efficiency while fulfilling a minimal set of constraints. The CFD model contains both important geometric features like tip gaps and fillets, and cooling and leakage flows to sufficiently represent real flow conditions. Two acceleration strategies are used to cut down the turn-around time from weeks to days. Firstly, the aerodynamic multi-stage design evaluation is significantly accelerated with a GPU-based RANS solver running on a multi-GPU workstation. Secondly, a response surface method is used to reduce the number of expensive function evaluations during the optimization process. The feasibility is demonstrated by an application to a blade which is a part of a research rig similar to the high pressure turbine of a small civil jet engine. The proposed approach enables an automatic aerodynamic design of this 3D blade on a single workstation within few days.

Concurrent Blade Aerodynamic-Aeroelastic Design Optimization With Re-Scaled Response Surface

Given the ever increasing demands on turbomachinery performance, various advanced blade shape optimizations have been actively developed and applied in modern blading designs. Multidisciplinary and concurrent optimizations have attracted considerable attention, offering the advantage of disciplinary interactions being included more simultaneously in a design process. This paper presents the development of a multidisciplinary optimization algorithm for the concurrent blade aerodynamic and aeromechanic shape optimization of realistic 3D turbine stages. A non-gradient algorithm is enhanced by a new re-scaled response surface (RSM) model. This meta-model is able to rescale the design space and redefine the response surface during a blade shape optimization process, leading to a much enhanced convergence compared to a standard RSM approach. The optimization algorithm is developed in conjunction with an efficient nonlinear harmonic phase solution method solving the unsteady flow equations in the frequency domain, combined with a finite element analysis (FEA) to extract the structural dynamic characteristics of the blades. The effectiveness of the concurrent method is examined for an optimized design of a realistic LP turbine stage. The optimization goals are the maximization of the isentropic stage efficiency and aeroelastic flutter stability (aero-damping). Two sets of cases are considered. In the first set, the shaping is applied only to stator blades, while for the second set, both stator and rotor blades are shaped. The concurrent cases are compared with their single-disciplinary counterparts. For both sets of the cases, the advantages of the concurrent treatment are clearly demonstrated.